Problem 4 [10 points total]. (a) [7 points] Determine the center of mass (CM) of a half circular disk of surface mass density o. Note that for a mass distribution

that is symmetric in regard to the z-axis, the Z component of the CM is given by Z=\frac{1}{M} \int z d m where, in this problem, M = 0 A and dm = odA–with A denoting the totalsurface area (area of half circular disk) and dA a surface element. (b) [3 points] Consider now a disk that consists of two parts: the upper half has a surface mass density 20 while the lower half has a surface mass density o. Determine the coordinate Z of the center of mass (CM) of this disk.